1. Field of the Invention
This invention is directed to well logging data interpretation systems and methods and, in one particular aspect, to a data inversion system and method that is usable at a well site to determine formation parameters and reservoir descriptions.
2. Description of Related Art
In certain prior art systems and methods well logging data is interpreted and evaluated to provide a picture or model of formations and of reservoirs to facilitate the removal of hydrocarbons, and to enhance the process of formation evaluation. Prior art well logging systems and methods provide a variety of data about formations through which the well extends; including, for example, resistivity data (induction and galvanic), acoustic data, vertical seismic profiling data, magnetic data, gravimetric data, temperature data, nuclear data, etc.
Inversion provides an estimate of the material properties of a formation by updating and improving an initial earth model, containing a material property description of the subsurface, with a better model until an optimal model is obtained. An instrument response numerically calculated from a model is compared to the response actually measured by instruments; if they match, the model is a correct one. If they do not match, the model is changed, to improve the match between what is measured and what is calculated from the model. The update of model parameters can be performed by known linear ("Inverse Problem Theory", Tarantola, 1987) or non-linear optimization methods ("Genetic Algorithms and Very Fast Simulated Annealing", Ingber and Rosen, 1992). Numerical calculation of well logging tool responses is relatively slow, even on powerful computers when using wave propagation, potential, nuclear or electromagnetic field theory.
Known two-dimensional (2-D) inversion techniques are used to interpret resistivity well logging data. These techniques simultaneously consider the borehole parameters, invasion parameters, and shoulder-bed effects with respect to a set of resistivity well logging measurements. However, certain conventional 2-D inversion techniques for such data require significant computer power and computational time and are not available at a well site.
The computational time required by certain known conventional 2-D inversion methods for well logging data based on linearized or non-linear inversion schemes grows very rapidly with the complexity of the earth model and the number of logging depths. For example, the well-known generalized least-squares technique (based on a local linearization of a non-linear inverse problem) requires performing very time-consuming multiple 2-D forward modeling at each iteration of the inversion procedure in order to calculate the Jacobian matrix (Stable iterative methods for the inversion of geophysical data: Geoph. J. Royal Astr. Soc., 42, 957-976, Jupp and Vozoff, 1975; A review of least-squares inversion and its application to geophysical problems: Geoph. Prosp., 32, 159-186, Lines and Treitel, 1984). This type of inversion technique is used for 2-D inversion of resistivity well logging data at stationary Log Analysis Centers. Some examples of applications of the generalized least-squares technique for 2-D inversion of resistivity logging data are presented in Integrated 2-D interpretation of resistivity logging measurements by inversion methods: Presented at the 36th Annual SPWLA Logging Symposium in June, 1995, Mezzatesta et al.
A rapid 2-D inversion method has been applied to Russian lateral resistivity (BKZ) logging data (About one iterative algorithm for solving two-dimensional inverse problem of logging by lateral sounding: Geology and Geophysics, 9, 118-123, Druskin and Knizhnerman, 1987). A similar method was applied to magnetotelluric data (Rapid inversion of two- and three-dimensional magnetotelluric data: J. Geoph. Res., 96,3905-3922, Smith and Booker, 1991).
The inversion of logging data determines the distribution of resistivity around a borehole in both the radial and vertical directions. The results of the inversion are normally presented in terms of a sequence of N layers, each one identified by its thickness and radial distribution of resistivities (step profile, annulus, ramp, etc.). One rapid 2-D method for processing data for a formation is an iterative procedure, each iteration consisting of the following steps as shown in FIG. 1: i) An initial earth model is developed based on raw data ("Set Initial Earth Model") and the 2-D forward modeling based on the initial earth model is done to calculate synthetic tool responses to produce synthetic data "Compute one time 2-D responses (1 depth per layer)"!; ii) if a misfit between raw actual data and synthetic data from the model ("COMPUTE DATA MISFIT") is acceptable ("Misfit accepted ? yes") the model is accepted ("END"); if not ("no", iii) calculate N times (N=number of layers in the formation under study) (one-dimensional) responses at each layer (assuming the layer is infinitely thick, i.e. no layers above or below it) "Compute N times 1-D tool response (using numerical modeling)"!; (iv) a correction "Perform data correction (shoulder bed correction)"! of the logging data is done for shoulder bed effects based on formation parameters obtained from previous steps; v) N times 1-D inversions using numerical forward modeling procedures are done, for each layer (second lowest box, FIG. 1), using the corrected field data from the previous step "Perform N times 1-D inversion (using numerical modeling)"!. Each iteration (i-v, above) provides a new set of formation parameters ("Update Earth Model"). The iterative cycle is repeated until the misfit between synthetic and raw (measured, without any correction) data becomes less than some predetermined acceptable small value (e.g. within the range of uncertainty of the data, typically 5% or less). Following the 1-D inversions of corrected data, the corrected 1-D earth model parameters for each layer are combined in a new, and possibly finally, 2-D earth model. This 2-D earth model is then subjected to the 2-D FORWARD MODELLING and 1-D FORWARD MODELLING steps and, if it is acceptable, the process ends ("END") with a new earth model. The rapid 2-D inversion requires less computational time than certain conventional techniques; however, both the conventional and the rapid 2-D inversion methods alone do not make well logging data inversion practical at a well site. Overcorrection is a known numerical calculation technique (see, e.g., .sctn.19.5, Numerical Recipes in Fortran, Press et al, Cambridge Univ. Press, Second Edition, 1992, incorporated fully herein by reference, pp. 854-860).
There has long been a need, recognized by the present inventors, for a well logging data interpretation system and method useful at a well site. There has long been a need for such a system and method in which required computation time is significantly reduced. There has long been a need for such a system and method which is able to take into account significantly more data and more types of different data related to a formation under study.